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• Open Access   Article

  Total Neighborhood Magic Labeling for Complete Graph, Path and C_n?K_1

  N P Shrimali, Y M Parmar, M A Patel

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.3 , pp.1-5, Jun-2024

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  — A bijection f:V(G)? E(G)? {1,2,…,|V(G)? E(G)|} is a total neighborhood magic labeling on a graph G with vertices n and edges e such that ?_(v?N(u))??(f(v) ?+f(uv))=k, ? u?V(G), where N(u) is the set of all adjacent vertices of u in V(G). Here k is the magic constant of total neighborhood magic graph and graph G is known as a total neighborhood magic graph. In this paper, we examine a total neighborhood magic labeling for complete graph with odd vertices, path and corona product between C_(n )& K_1.

  Key-Words / Index Term
  Complete graph, path, corona product, total neighborhood magic labeling

  References
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  [7] B. D. Acharya, S. B. Rao, T. Singh and V. Parameswaran, “Neighborhood magic graphs”, National Conference on Graph Theory, Combinatorics and Algorithm, 2004.
  [8] N. P. Shrimali and Y. M. Parmar, “Total Neighborhood Magic Labeling: A New Variant of Magic Labeling”, Turkish Journal of Computer and Mathematics Education, Vol.12, Issue.13, pp.6693-6702, 2021
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  [10] H. K. Krishnappa, K. Kothapalli and V. CH. Venkaiah, “Vertex magic total labeling of complete graphs”, AKCE Journal of Graphs and Combinatorics, Vol.6, Issue.1, pp.143-154, 2009.

  Citation
  N P Shrimali, Y M Parmar, M A Patel, "Total Neighborhood Magic Labeling for Complete Graph, Path and C_n?K_1," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.3, pp.1-5, 2024

• Open Access   Article

  Length-Biased Distribution for Family of Life-Time Testing Models and its Properties

  Surinder Kumar, Shivendra Pratap Singh, Bhupendra Meena, Rahul Shukla

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.3 , pp.6-13, Jun-2024

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  Our research introduces a new lifetime distribution family called Length-Biased Lifetime Distribution, which is based on length bias. To comprehend the nature of the suggested distribution, we take into account its many statistical aspects, such as its reliability, hazard function and other characteristics. Also, to estimate the parameters of the suggested distribution, we have utilized the ML technique. The Lorenz and Bonferroni curves, Shannon’s entropy, and Renyi entropy are also obtained. Using two real-life datasets, we evaluate the suggested distribution’s performance to that of competing distributions.

  Key-Words / Index Term
  Entropy, Hazard Function, Length-Biased Distribution, Maximum Likelihood Estimation, Reliability, Reversed Hazard Function, Order Statistic.

  References
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  [9] A. A. Dar, A. Ahmed, and J. A. Resh, “An extension of power distribution,” Investigación Operacional, Vol.39, Issue.4, pp.626–638, 2018.
  [10] A. A. Rather, and C. Subramanian, “Length-biased Sushila distribution,” Universal Review, Vol.7, Issue.12, pp.1010–1023, 2018.
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  [12] A. Malik, and S. Ahmad, “A New inverse Rayleigh distribution: Properties and application,” Int. J. Sci. Res. in Mathematical and Statistical Sciences, Vol.5, Issue.5, pp.92–96, 2018.
  [13] Y. Atikankul, A. Thongteeraparp, W. Bodhisuwan, and A. Volodin, “The length-biased weighted Lindley distribution with applications,” Lobachevskii Journal of Mathematics, Vol.41, pp.308–319, 2020.
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  [15] A. I. Al-Omari, R. Alsultan, and G. Alomani, “Asymmetric Right-Skewed Size-Biased Bilal Distribution with Mathematical Properties, Reliability Analysis, Inference and Applications,” Symmetry, Vol.15, Issue.8, pp.1578, 2023.
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  [17] O. Y. Sule, and O. Y. Halid, “On Gompertz Exponentiated Inverse Rayleigh Distribution,” Reliability: Theory & Applications, Vol.1, Issue.72, pp.412-422, 2023.
  [18] A. Alzaatreh, F. Famoye and C. Lee, “The gamma-normal distribution: Properties and applications,” Quality control and applied statistics, Vol.60, Issue.1, pp.119-120, 2015.
  

  Citation
  Surinder Kumar, Shivendra Pratap Singh, Bhupendra Meena, Rahul Shukla, "Length-Biased Distribution for Family of Life-Time Testing Models and its Properties," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.3, pp.6-13, 2024

• Open Access   Article

  Numerical Simulation of Mixed Convection in Three Sided Lid Driven Cavity

  Arti Kaushik

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.3 , pp.14-25, Jun-2024

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  Abstract
  In this article mixed convection in an incompressible, 2D, steady state, Newtonian fluid flow in a three sided lid driven cavity is studied using finite volume method and Semi Implicit Method for Pressure Linked Equations (SIMPLE) technique. The top and bottom walls (North and South walls) move in same direction whereas the right vertical wall (East wall) moves in upward direction. The left vertical sidewall (West wall) is stationary. A detailed analysis of the fluid flow has been carried out for different values of density and viscosity of fluid for varied values of wall velocity. The results are displayed in terms of velocity profiles, pressure and temperature contours and in accord with the set of literature.

  Key-Words / Index Term
  Three sidedlid driven cavity, incompressible flow, mixed convection flow, SIMPLE algorithm

  References
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  [7] Charles-Henri Bruneau, Mazen Saad, “The 2D lid-driven cavity problem revisited”,Computers & Fluids,Vol.35, Issue.3, pp.326-348, 2006.
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  [11] C H. Blohm and H. C. Kuhlmann,” The two-sided lid-driven cavity: experiments on stationary and time-dependent flows”, Journal of Fluid Mechanics, Vol.450, pp.67 – 95, 2002
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  [14] E.M. Wahba,” Multiplicity of states for two-sided and four-sided lid driven cavity flows“, Computers & Fluids , Vol. 38, Issue 2, pp 247-253, 2009.
  [15] Dedy Zulhidayat Noor, P. Rajesh Kanna, Ming-JyhChern, “Flow and heat transfer in a driven square cavity with double-sided oscillating lids in anti-phase” International Journal of Heat and Mass Transfer, Vol. 52, Issue13-14, pp 3009-3023, 2009.
  [16] AdekojoWaheed, “Mixed convective heat transfer in rectangular enclosures driven by a continuously moving horizontal plate ”,International Journal of Heat and Mass Transfer, Vol. 52, Issue 21, pp 5055-5063, 2009
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  [18] K.-T. Chen, C.-C.Tsai, W.-J.Luo & C.-N. Chen ,” Multiplicity of steady solutions in a two-sided lid-driven cavity with different aspect ratios”, Theor. Comput.Fluid Dyn. , Vol 27, pp 767–776 2013.
  [19]Fayçal Hammami, Basma Souayeh, Nader Ben Cheikh, Brahim Ben-Beya, “Computational analysis of fluid flow due to a two-sided lid driven cavity with a circular cylinder”,Computers& Fluids, Vol.156, pp.317-328, 2017.
  [20] Abanoub G. Kamel, Eman H. Haraz, and Sarwat N. Hanna,” Simulation of Three-Sided Lid-Driven Cavity”, International Journal of Modeling and Optimization, Vol.10, No.2, 2020.
  [21]El Amin Azzouz & Samir Houat,”Numerical Solutions of Steady Flow in a Three-Sided Lid-Driven Square Cavity”,International Journal of Applied and Computational Mathematics , Vol.8, No.118, 2022.
  [22] KuenTsann Chen, Chih Ching Tsai, Win Jet Luo,”Multiplicity Flow Solutions in a Four-Sided Lid-Driven Cavity”,Applied Mechanics and Materials, Vols. 368-370, pp.1372, 2021
  [23] Cheng Gong Li and Jerome P-Y Maa, “Lattice Boltzmann simulations of three-dimensional incompressible flows in a four-sided lid driven cavity”, Fluid Dynamics Research, Vol.49, No.2, 2017.
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  Citation
  Arti Kaushik, "Numerical Simulation of Mixed Convection in Three Sided Lid Driven Cavity," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.3, pp.14-25, 2024

• Open Access   Article

  Utilizing CART Classification Decision Tree Model to Examine Unemployment Trend in Nigeria

  Lekia Nkpordee, Juma Ndhokero

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.3 , pp.26-37, Jun-2024

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  Abstract
  This particular study utilizes CART classification decision tree models to examine thirty - three years of unemployment information in Nigeria, derived from the World Bank along with the International Labour Organization. Using extensive statistical tests, such as the BDS test for nonlinearity, the ADF device root test for stationarity, and the Breusch Pagan test for heteroscedasticity, the research validates the value of the CART design for understanding the complex dynamics of unemployment in Nigeria. Important elements including household income, the industry sector in addition to education are identified and also highlighted their importance in determining unemployment rates. Results demonstrated the sequence of unemployment rates is stationary yet nonlinear, highlighting the complicated nature of unemployment dynamics. CART models display substantial predictive accuracy, discover considerable predictors of unemployment, and also offer insights for policy formulation. This research plays a role in the literature by introducing a novel approach to examining unemployment rates in Nigeria and stresses the need for innovative analytical methods to tackle socioeconomic challenges.

  Key-Words / Index Term
  CART Classification, Decision Tree Model, Examination, Machine Learning, Unemployment, Trend

  References
  [1] R. A. Aregbeshola and P. O. Ogunjuyigbe, "Determinants of unemployment in Nigeria: Empirical insights from ARDL bounds testing approach," Cogent Economics & Finance, Vol.8, No.1, pp.1805027, 2020.
  [2] V. A. Odozi, "Education and youth unemployment in Nigeria: A quantitative assessment," International Journal of Social Economics, Vol.46, No.6, pp.773-789, 2019.
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  [4] E. B. Udah and O. E. Etim, "Analysis of the determinants of unemployment in Nigeria: Evidence from ordinary least squares and cointegration approach," Journal of Economics and Sustainable Development, Vol.9, No.2, pp.85-97, 2018.
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  [6] J. Smith and K. Johnson, "Exploring factors influencing unemployment rates in the United States: A CART classification decision tree analysis," Journal of Economic Studies, Vol.36, No.2, pp.12-29, 2019.
  [7] L. Wang and H. Liu, "Determinants of urban unemployment in China: Insights from CART classification decision tree models," International Journal of Social Economics, Vol.43, No.4, pp.1-18, 2020.
  [8] A. Khan and S. Ali, "Analyzing rural unemployment determinants in Pakistan: A CART classification decision tree approach," Journal of Development Studies, Vol. 55, No.3, pp.25-38, 2018.
  [9] T. T. Adeliyi1, L. Oyewusi, A. Epizitone, and D. Oyewusi, "Analysing factors influencing women unemployment using a random forest model," Hong Kong Journal of Social Sciences, Vol.60, No.1, pp.382-393, 2023.
  [10] I. A. Ogunsola, O. M. Olayiwola, and B. O. Sowola, "Modeling unemployment rates in Nigeria using time series approach," Asian Journal of Mathematical Science, Vol.4, No.2, pp.1-6, 2020.
  [11] T. S. Mohammad, "Dynamics of unemployment and economic growth on terrorism in Nigeria-Evidence from a linear quantile modelling approach," JEL classification; Vol.24, No.64, pp.1-9, 2022.
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  [13] I. J. Ubah, E. Bowale, O. J. Ejemeyovwi, and Y. Okereke, "Effects of technological diffusion and access to electricity on employment in Nigeria," International Journal of Energy Economics and Policy, Vol.11, No.2, pp.227-233, 2021.
  [14] B. O. Akin-Awoniran, S. O. Jabaru, and K. Jimoh, "Parametric modelling of impact of unemployment on economic growth in Nigeria," International Journal of African and Asian Studies, Vol.13, pp.102-109, 2015.
  [15] A. Gerunoy, "Employment modelling through classification and regression trees," Journal of data science, Vol.1, No.4, pp.316-329, 2016.

  Citation
  Lekia Nkpordee, Juma Ndhokero, "Utilizing CART Classification Decision Tree Model to Examine Unemployment Trend in Nigeria," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.3, pp.26-37, 2024

• Open Access   Article

  Exploring Orientability: An Investigation of the Mobius Strip Using Cut and Paste Technique

  Akanksha Singh, Garima Singh, Anshu Singh

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.3 , pp.38-42, Jun-2024

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  Abstract
  The Möbius strip carries the pure and essential example of non-orientable manifold, presents a challenge in understanding its inherent properties. This research investigates the orientability of the Möbius strip through a new approach. Our study aims to explore the possibility of altering the Möbius strip’s topology through cutting and pasting . We employ a combination of geometric visualization, topological manipulation, and mathematical analysis to systematically dissect Möbius strip and perform surgical modifications and reassemble the resulting structures. Through this process, we examine the consequences of each cutting and pasting operation on the orientability of the Möbius strip and explore how these actions affect its orientability. We will employ known results of topology and differential geometry methods to prove orientability of cut and pastes of Möbius strip.

  Key-Words / Index Term
  Differential Topology, Differential geometry, Möbius strip, Orientable, Non-Orientable Manifold

  References
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  Citation
  Akanksha Singh, Garima Singh, Anshu Singh, "Exploring Orientability: An Investigation of the Mobius Strip Using Cut and Paste Technique," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.3, pp.38-42, 2024

• Open Access   Article

  Exact Solitary Wave Solution of Benjamin-Bona-Mahony and Modified Regularized Long Wave Equations Using Sardar Subequation Method

  Lawwal Muduru Sada, Umar Ali Muhammad, Musa Idris

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.3 , pp.43-49, Jun-2024

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  Abstract
  This article explores solutions for the Benjamin-Bona-Mahony (BBM) equation and the Modified Regularized Long Wave (MRLW) equation. The BBM equation serves as a model for the propagation of small-amplitude long waves in one-dimensional space, addressing limitations of the classic Korteweg-de-Vries (KdV) equation, particularly in high wavenumber scenarios. On the other hand, the MRLW equation describes dispersed wave phenomena, such as those observed in shallow water and phonon packets within nonlinear crystals. The solutions to these equations manifest as solitary waves, commonly known as solitons. In this study, we employ the improved Sardar subequation method to comprehensively analyze the resulting solitary waves. We also provided the visual representations for obtained solutions in the forms of absolute value 3D, 2D, and contour plots.

  Key-Words / Index Term
  BBM equation, MRLW equation, improved Sardar subequation method, solitary wave, KdV, Shallow water wave

  References
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  [18] M. Ramli, D. Irsalina, I. P. Iwanisa, and V. Halfiani, "Soliton solution of Benjamin-Bona-Mahony equation and modified regularized long wave equation," in AIP Conf. Proc., AIP Publishing, Dec. Vol.1913, No.1, 2017.
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  [23] A. K. Khalifa, K. R. Raslan, and H. Alzubaidi, "Numerical study using ADM for the modified regularized long wave equation," Appl. Math. Model., Vol.32, No.12, pp.2962-2972, 2008.
  [24] A. Kumar and R. Arora, "Soliton Solution for the BBM and MRLW Equations by Cosine-function Method," in Adv. Model. Optim. Comput., pp. 49, 2011.
  [25] Z. U. A. Zafar, "Soliton Solution of IMKDV, KDV, GKDV and MRLW Equations by Sine-hyperbolic Function Method," Int. J. Adv. Eng. Glob. Technol., Vol.1, No.3, 2013.
  [26] L. Akinyemi, "Two improved techniques for the perturbed nonlinear Biswas–Milovic equation and its optical solitons," Optik, Vol.243, pp.167477, 2021.
  

  Citation
  Lawwal Muduru Sada, Umar Ali Muhammad, Musa Idris, "Exact Solitary Wave Solution of Benjamin-Bona-Mahony and Modified Regularized Long Wave Equations Using Sardar Subequation Method," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.3, pp.43-49, 2024

• Open Access   Article

  A Comparative study about pi in various ancient civilization and it’s present scenario

  Neha Choubey, Garima Singh, Anshu Singh

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.3 , pp.50-56, Jun-2024

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  Abstract
  Presently, blockchain-powered cryptocurrency has gained widespread recognition. Bitcoin stands out as one of the most valuable and sought-after digital currencies. However, Bitcoin`s accessibility is limited across various platforms, and its user-friendliness leaves much to be desired. Nonetheless, a new user-friendly cryptocurrency is on the horizon. Pi Coin aims to cater to a broader audience, potentially revolutionizing the future cryptocurrency landscape. While Bitcoin has already established its demand in the crypto sphere, Pi Coin is generating considerable buzz as it prepares for launch. This paper will explore the projected value of Pi Coin based on the timeline of Bitcoin`s development.

  Key-Words / Index Term
  Blockchain, cryptocurrency, Bitocoin, Pi Network

  References
  [1] R. Merkle, “Protocols for public key cryptosystems,” in Proceeding of the 1980 Symposium on Security and Privacy, IEEE Computer Society, pp. 122-133, April 1980.
  [2] F. Tschorsch and B. Scheuermann, “Bitcoin and beyond: a technical survey on decentralized digital currencies,” IEEE Communications Surveys & Tutorials, vol.18, pp.2084-2123, March 2016.
  [3] J. Douceur, “The Sybil attack,” in Proceedings of IPTPS `01 Revised Papers from the First International Workshop on Peer-to-Peer Systems, pp. 251-260, March 2002.
  [4] S. Barber, X. Boyen, E. Shi and E. Uzun, "Bitter to better—How to make bitcoin a better currency", Proc. 16th Int. Conf. Financial Cryptogr. Data Secur. (FC’12), pp. 399-414, Mar. 2012.
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  [6] Rosario Gennaro, Stanislaw Jarecki, Hugo Krawczyk, Tal Rabin, “Secure Distributed Key Generation for Discrete-Log Based Cryptosystems”, Proc. Of the 17th Int. Conf. on Theory and application of cryptographic techniques, May 2005.
  [7] A. Biryukov, D. Khovratovich, “Equihash: asymmetric proof-of work based on the generalized birthday problem,” Ledger, vol. 2, pp. 1-30, April 2017.
  [8] Md. Mahfuzul Islam Shamim “IT Skills Development Project and Economic Development in Bangladesh”, Academic Journal of Digital Economics and Stability, vol. 19(7), pp.13-21, July 2022.
  [9]K.M.Samin, Bijoy Kumar Deshmukhya, Farhan Bin Alam, "A Brief analysis on predicted future value of pi network on the basis of bitcoin", Global Mainstream Journal of Innovation, Engineering & Emerging Technology, October 2022.
  [10] D. Malkhi and M. Reiter, “Byzantine quorum systems,” Distributed Computing, vol. 11, pp. 203-213, October 1998.

  Citation
  Neha Choubey, Garima Singh, Anshu Singh, "A Comparative study about pi in various ancient civilization and it’s present scenario," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.3, pp.50-56, 2024

• Open Access   Article

  Fractional Mathematical Modeling of Ternary Nanofluid Flow Through an Inclined Artery

  Hamza Saleh Zakari, Aminu Barde, Isah Abdullahi

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.3 , pp.57-63, Jun-2024

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  In this study, we examined the fractional order flow of Casson tri-nanofluid through an inclined artery, integrating gold (Au), copper (Cu), and alumina (Al2O3) nanoparticles into blood to form the tri-nanofluid. The flow was modelled as highly pulsatile. The mathematical formulation used differential forms of the conservation laws of mass, momentum, and energy, with the electric potential along the arterial wall accurately described by the Poisson-Boltzmann equation. The classical problem was converted into its fractional equivalents using the Caputo time-fractional derivative. Exact solutions for these transformed equations were derived using a combination of Laplace and finite Hankel transforms, with results computed and graphically presented using Mathcad software. The purpose of incorporating the tri-nanofluid was to enhance heat transfer by improving the fluid`s thermal conductance. The findings revealed that the velocity profiles of the blood flow decreased with an increasing radiation parameter, while the opposite effect was observed with increasing porosity parameter. The temperature profile arose with higher fractional parameter values. This study holds potential for applications in targeted drug delivery using magnetic nanoparticles

  Key-Words / Index Term
  Nano Particles, Inclined Artery, Ternary nanofluid, Time-Fractional Derivative

  References
  [1] W. Tan and T. Masuoka, "Stokes` First Problem for a Second Grade Fluid in a Porous Half-Space with Heated Boundary,"International Journal of Non-Linear Mechanics, vol. 40, pp. 515-522, 2005.
  [2] C. Fetecau, D. Vieru, and C. Fetecau, "On Some Herical Flows of Oldroyd-B fluids," Acta Mechanica, vol. 189, pp. 53-63, 2007.
  [3] D. Vieru, T. Hayat, C. Fetecau, and C. Fetecau, "On the first problem of Stokes for Berger`s fluids. II: The case ??((?²)/4) and ?>((?²)/4)," Applied Mathematics and Compututation, vol. 197, pp. 76-86, 2008.
  [4] Z. Ziabakhsh and G. Domairry, "Analytical Solution of Natural Convection Flow of a Non-Newtonian Fluid Between Two Vertical Flat Plates Using Homotopy Analysis Method," Communication in Nonlinear Science and Numerical Simulation, vol. 14, pp. 1868-1880, 2009.
  [5] T. Hayat, R. Naz, and M. Sajid, "On the Homotopy Solution for Poiseuille Flow of a Fourth Grade Fluid," Communications in Nonlinear Science and Numerical Simulation, vol. 15, pp. 581–589, 2010.
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  [8] K. M. Sharma, K. Bansal, and S. Bansal, "Pulsatile unsteady flow of blood through porous medium in a stenotic artery under the influence of transverse magnetic field," Korean-Australian Rheology Journal, vol. 24, no. 3, pp. 181-189, 2012.
  [9] N. Shavastava, "Analysis of flow characteristics of the blood flowing through an inclined tapered porous artery with mild stenosis under the influence of an inclined magnetic field," Journal of biophysics, vol. 9, p. 797142, 2014.
  [10] D. Kumar, B. Satyanarayana, K. Rajesh, D. Narendra, and K. Sanjeev, "Application of heat source and chemical reaction in magnetohydrodynamic blood flow through permeable bifurcated arteries with inclined magnetic field in tumor treatments," Journal of Result in Applied Physics, vol. 10, no. 100151, pp. 1-13, 2021.
  [11] E. E. Tzirtzilakis, "A mathematical model for blood flow in magnetic field," Physics of Fluids, vol. 17, no. 7, pp. 077-103, 2005.
  [12] E. E. Tzirtzilakis, "Biomagnetic fluid flow in a channel with stenosis," Physica D: Nonlinear Phenomena, vol. 237, no. 1, pp. 66-81, 2008.
  [13] M. A. Ikbal, S. Chakravarty, K. K. Wong, J. Mazumdar, and P. K. Mandal, "Unsteady response of non-Newtonian blood flow through a stenosis artery in magnetic field," Journal of Computational and Applied Mathematics, vol. 230, no. 1, pp. 243-259, 2009.
  [14] I. Pishkar, B. Ghasemi, A. Raisi, and S. M. Aminossadati, "Natural Convective Heat Transfer of Magnetite/Graphite Slurry Under a Magnetic Field," Journal of Thermo-physics and Heat Transfer, pp. 1-13, 2019.
  [15] T. Nazar and M. S. Shabbir, "Irreversibility analysis in the ternary nanofluid flow through an inclined artery via Caputo-Fabrizio fractional derivatives," Results in Physics, pp. 2211-3797(23)00785-4, 2023.
  [16] J. C. Chato, "Heat transfer to blood vessels," Journal of Biomechanical Engineering, vol. 102, no. 2, pp. 110–118, 1980.
  [17] S. Shaw and P. V. S. N. Murthy, "Magnetic drug targeting in the permeable blood vessel: the effect of blood rheology," Journal of Nanotechnology in Engineering and Medicine, vol. 1, no. 2, pp. 021001–021011, 2010.
  [18] S. Maiti, S. Shaw, and G. C. Shit, "Caputo–Fabrizio fractional order model on MHD blood flow with heat and mass transfer through a porous vessel in the presence of thermal radiation," Physica A: Statistical Mechanics and its Applications, vol. 540, p. 123149, 2020.
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  Citation
  Hamza Saleh Zakari, Aminu Barde, Isah Abdullahi, "Fractional Mathematical Modeling of Ternary Nanofluid Flow Through an Inclined Artery," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.3, pp.57-63, 2024

• Open Access   Article

  A Mathematical model of Psoriasis disease using a good diet (turmeric incorporated ) as a method to control the disease

  Munira Salisu, M.S. Atureta, Manga M.M.

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.3 , pp.64-68, Jun-2024

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  Abstract
  In this study, the method of control of psoriasis by using a good diet with turmeric incorporated, was adopted to have a better means of controlling the skin infection. The modification of the Nirmelendu and Biplap(2012) was modified,as the mathematical model contains three system of differential equations. From previous study and biological point of view, the skin comprises of the the three components such as the leucocytes, Keratinocytes and proteins hence the formulation of the equations based on the mentioned. When modelling, certain assumptions were put forth to formulate the three equations. A local stability analysis was considered to obtain a disease free equilibrium. This was obtain by the Jacobian matrix.Conclusively, The hyperactivity of the keratinocytes is being moderated by the turmeric which slows the activity of the proteins to signify the keratinocytes.

  Key-Words / Index Term
  Psoriasis,Proteins,Keratinocytes,Leucocytes,Tcells,Chemokynes,Jacobian matrix, Disease free equilibrium, local stability, Immuno pathogenesis.

  References
  [1] A.D. Omerod,C.M.Pwyer, R. Weller,D.H Cox and R.Rice, ‘’A comparison of subjective and objective measures of reduction of psoriasis with the use of ultrasound reflectance colomeritry computerized video image analysis and nitric oxide production,’’ Journal of dermatological sciences, Volume 3,7 issue ,1 pp. 51-57, 1997.
  [2] A. Ovide and M. Kimmel, ‘’Stability analysis of model of cell production systems,’’ Journal of mathematical biology, Vol.7, No 1, pp. 1269-1300, 1988.
  [3] B. Chattopadhyay and H. Nirmelendu ‘’Immuno pathogenesis in psoriasis through a density type mathematical model,’’ WSEAS transaction on mathematics Journal Benghal India,Vol. 11, 1sue 5, pp. 456-466, 2012.
  [4] J.E. Gudjonsson, A. Johnston, H. Signunsidottir and H. Vladimarsson, ‘’Immuno pathogenesis mechanism in psoriasis,’’ Journal of the American academy of allergy, asthma and immunology Elsevier, Vol.135, no1, pp. 1-8, 2004.
  [5] K.Atittey and B. Achang, ‘’A model based evaluation of spatio temporal data reduction methods with unkown ground truth through optimal visualization and interpretability metrics,’’ Breifings in Bioinformatics, 2024.
  [6] K. Neils and K. Neuber, ‘Stimulating psoriasis by altering transit amplifying cells,’’Jjournal of Bioinformatics and computer science, Vol. 23, issue 11, pp. 1309-1312, 2007.
  [7] P. Kumar, J. Bhandra and B. Chattopadhayay ‘‘mathematical modeling on immune pathogenesis in chronic plague of psoriasis: a theoretical study,’’ proceedings of the world congess on engineering 2010 WCE 2010, Vol. 1, pp. 1-6, 2010.
  [8] Y. Lin, A. Huang, C. Yi-Yang and W. Chang, ‘’measurement of body surface area for Psoriasis using U- net models,’’ Journal of computational and mathematical methods in medicine, Vol.2, No 7, pp. 1-9, 2021.

  Citation
  Munira Salisu, M.S. Atureta, Manga M.M., "A Mathematical model of Psoriasis disease using a good diet (turmeric incorporated ) as a method to control the disease," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.3, pp.64-68, 2024

• Open Access   Article

  Integrating Discrete Mathematics in artificial intelligence: A computational perspective with a vision for future technologies

  Shalini Mishra, Garima Singh, Manju Prabhakar

  Research Paper | Journal-Paper (IJSRMSS)

  Vol.11 , Issue.3 , pp.69-74, Jun-2024

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  Abstract
  This paper present a comprehensive examination of the fundamental role that discrete mathematics plays in the development and future evolution of artificial intelligence(AI) by dissective the core components of AI systems through the lens of discrete mathematics, including areas such as graph theory, combinatoris, logic, and set theory, we identify pivotal connection and propose innovative pathways for future research. The goal is to illuminate how discrete mathematics concept can fuel advancements in AI, enhancing its efficiency, reliability and capability to solve complex problems this paper explores the application of discrete mathematics in the development and optimization of artificial intelligence algorithm and systems Through a series of calculative examples, we aim to illustrate the practical utility of discrete mathematical principles in enhancing the efficiency, accuracy and functionality of AI technologies.

  Key-Words / Index Term
  Artificial Intelligence; Discrete Mathematics; Graph Theory; Combinatorics in AI

  References
  [1] Chen, L., & Gupta, S.Discrete Mathematics in Artificial Intelligence: A Comprehensive Review Journal Artificial Intelligence and Discrete Mathematics, Vol.7,Issue.2, pp112-130, 2023.
  [2] F. Glover, Future Paths for Integer Programming and Links to Artificial Intelligence, Computers and Operations Research, Vol.13, Issue.5, pp.533-549, 1986.
  [3] Gendreau, M., Hertz, A., & Laporte, G. A review of heuristics for the vehicle routing problem. Operations Research, Vol.44, Issue.3, pp378-400, 1996.
  [4] Hopfield, J. J. Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences, Vol.79, Issue.8, pp2554-2558, 1982.
  [5] Hopfield JJ., Tank DW., “Neural” computation of decisions in optimization problems Biological Cybernetics, Vol.52, Issue.3, pp141-152, 1985.
  [6] Kennedy, M. P., & Chua, L. O. Neural networks for nonlinear programming. IEEE Transactions on Circuits and Systems, Vol.35, Issue.5, pp554-562, 1988.
  [7] Laporte, G. The traveling salesman problem: An overview of exact and approximate algorithms. European Journal of Operational Research, Vol.59, Issue.2, pp231-247, 1992.
  [8] Patel, R., & Wang, Graph-Theoretic Approaches to Machine Learning: A Survey , Journal of Artificial Intelligence and Discrete Mathematics Vol.5, Issue.3, pp201-220, 2022.
  [9] Smith, K., & Lee, T. H. Continuous-time neural networks for combinatorial optimization. IEEE Transactions on Circuits and Systems I: Regular Papers, Vol.55, Issue.8, pp2451-2461, 2008.
  [10] Yang, S., et al. On the convergence of a class of continuous time stochastic processes. IEEE Transactions on Automatic Control, Vol.62, Issue.12, pp6534-6549, 2017.

  Citation
  Shalini Mishra, Garima Singh, Manju Prabhakar, "Integrating Discrete Mathematics in artificial intelligence: A computational perspective with a vision for future technologies," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.3, pp.69-74, 2024